MHT CET · Physics · Magnetic Effects of Current

A circular coil of wire consisting of 100 turns each of radius 9 cm carries a current of 0.4 A. The magnitude of the magnetic field at the centre of coil is $[μ_{0} = 12.56 \times 10^{- 7} SI Units]$

A $2.4 \times 10^{- 11} T$
B $2.79 \times 10^{- 5} T$
C $2.79 \times 10^{- 4} T$
D $2.79 \times 10^{- 3} T$

Verified Solution

Answer & Solution

Correct Answer

(C) $2.79 \times 10^{- 4} T$

Step-by-step Solution

Detailed explanation

Given, number of turns, n = 100, radius of coil,

r = 9 c m = 9 \times 10^{- 2} m

and current flow in the coil, I =0.4 A
The magnitude of the magnetic field at the centre of a coil of n turns is given by

B = \frac{μ 0 n l}{2 r}

…. (i)
Substituting given values in Eq. (i), we get

\Rightarrow B = \frac{1256 \times 10^{- 7} \times 100 \times 0.4}{2 \times 10^{- 1} \times 9 \times 10^{- 2}}

= 2.79 \times 10^{- 4} T

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A circular coil of wire consisting of 100 turns each of radius 9 cm carries a current of 0.4 A. The magnitude of the magnetic field at the centre of coil is [ μ 0 =12.56× 10 −7 SI Units ]

Step-by-step Solution

A circular coil of wire consisting of 100 turns each of radius 9 cm carries a current of 0.4 A. The magnitude of the magnetic field at the centre of coil is $[μ_{0} = 12.56 \times 10^{- 7} SI Units]$